AucusT 27, 1914| 
NATURE 
683 
dence of its correctness—it indicates, for instance, that 
in crystalline potassium sulphate, if the atomic volume 
of potassium is taken as unity, those of sulphur and 
oxygen each have the value two. Many different lines 
of crystallographic argument converge, however, to 
this law, and, if the latter is in the end found to be 
incorrect, it at least represents something fundamentai 
which still awaits enunciation in a more generally 
acceptable form. A few illustrative instances may be 
quoted. 
If valency be a volume property, the relation should 
be revealed in the compositions of chemical substances, 
especially those of composite character. The sum of 
the valencies in potassium sulphate, K,SO,, is 12, and 
in ammonium sulphate, (NH,),SO,, 24, just twice the 
number; the two substances are so closely related 
that they crystallise together to form ‘“‘ solid solutions ”’ 
(isomorphous mixtures. Similarly, in the alums, such 
as K,SO,+Al,(SO,),+24H,O, the valencies are 
12+36+96; the sum of the valencies of the water 
present, 96, is just twice that, 48, of those exhibited 
by the metallic sulphates. Similar curious numerical 
relationships occur in each of the well-defined series 
of double salts. 
Again, if the valency volume law hold for two 
substances of different crystalline form, such as ortho- 
rhombic rubidium nitrate, RbNO,, and rhombohedral 
sodium nitrate, NaNO,, the metal, the nitrogen and 
the oxygen in each compound should have the re- 
spective atomic volumes, 1, 3, and 2. As the sub- 
stances differ in density the absolute values of the 
atomic volumes of nitrogen and oxygen will differ in 
the two substances as examined in the same tempera- 
ture; the ratios of the atomic volumes in either com- 
pound should, however, be as stated. Considering 
this conclusion in conjunction with the fact that these 
crystalline compounds represent symmetrically con- 
structed assemblages, it would seem that the relative 
dimensions of the one crystal structure should be 
traceable in those of the other. Orthorhombic rubi- 
dium nitrate exhibits the axial ratios, a:b:c= 
1-7336: 1: 0-7106, three rectangular coordinates, a, b, 
and c, being used as the directions of reference; 
rhombohedral sodium nitrate exhibits a:c=1 : 0-8276, 
the coordinates being three axes, a, making angles 
of 120° in one plane, and a fourth axis c, perpendicular 
to a. On converting the axial system of sodium 
nitrate into a simple set of rectangular axes similar 
to those used for rubidium nitrate, the value, a:c= 
1: 0:8276, becomes 
Ge bt G= 1-7520 27 5k. 
These values approximate very closely to those 
obtained by direct measurement of the orthorhombic 
rubidium salt. It seems difficult to avoid the con- 
clusion that the two diss‘milar crystalline structures 
are built up by the arrangement of layers or blocks of 
the same relative dimens’ons in two different ways, 
the molecule of sodium nitrate, NaNO,, possessing 
practically the same relative dimensions as that of 
rubidium nitrate, RbNO,; this, of course, is in dis- 
accord with the classic conception of atomic volume, 
but agrees entirely with the valency volume law. 
Another remarkable body of evidence is found in 
the interpretation of many morphotropic relationships 
between organic and inorganic substances which have 
been long recognised but have hitherto eluded inter- 
pretation. The description of one or two cases will 
make the bearing of the law of valency volumes clear 
in this connection. 
d-Camphoric anhydride, C,,H,,O,, and d-camphoric 
acid crystallised with acetone, C,,H,,O,, 1/2 (CH;),CO, 
NO. 2339, VOL. 93] 
both crystallise in the orthorhombric system and ex- 
hibit the axial ratios stated in the following Table 
II. :— 
Tasce II. 
W DB Ae} a yx z 
I‘OOIT : 1 3 1°7270 3°2654 : 3°2618 3 5°6331 
1°2386 21 34°7172 470435 : 3°2646 : 5°0000 
Ci9H 403... eee vee 160 
Cio H 1604, 1/2(CH3)2CO 74 
The ratio c/b is approximately the same in the two 
cases and general similarity exists between the two 
crystalline substances. It will be observed that the 
values of a/b are very nearly in the ratio of the sums 
of the valencies, W, making up the two molecular 
complexes, namely, 60:74=100: 123. This and 
similar cases may be more conveniently discussed with 
the aid of the so-called equivalence parameters; these 
are the edge lengths, x, y, and z, of a parallelepipedon 
of which the volume is W, the sum of the valencies in 
the molecule, and of which the linear and angular 
dimensions express the crystallographic axial ratios. 
Thus, for orthorhombic substance xyz=W, and 
x:y:z=a:b:c; the equivalence parameters of the 
two substances under discussion are given in the table, 
and it will be seen that whilst y and z are almost 
identical for the two, the z values differ considerably. 
This correspondence indicates clearly that in passing 
from camphoric anhydride to the acetone compound 
of the acid the mass added to the molecular complex, 
H,O0+1/2(CH,),CO, occupies a volume proportional 
to the number of valency units which its contributes to 
the structure. 
A very remarkable relation has been long recog- 
nised between the crystalline forms of the three 
minerals chondrodite, Mg,(SiO,),, 2Mg(F,OH), 
humite, Mg,.(SiO,),, 2Mg(F,OH), and clinohumite, 
Mg,(SiO,),, 2Mg(F,OH); the crystalline forms are 
referable to three rectangular directions, a, b, and c, 
and the ratio a: b is practically the same for all three 
minerals. The relationship is at once elucidated by 
the law of valency volumes in a simple manner. In 
the molecules of the three substances the sums of the 
valencies of the constituent atoms are respectively 
34, 48, and 62; it follows from the law that these 
numbers are proportional to the relative volumes of 
the several molecules. The ratios, a:b:c, being 
known, the dimensions can be calculated of solid 
rectangu'ar blocks having these volumes and having 
edge lengths proportional to the axial ratios, a:b: c. 
The equivalence parameters, x, y, and gz, thus cal- 
culated are given in the following Table III.; the first 
observation of importance to be made is that the 
equivalence parameters, x and y, remain practically 
constant throughout the series of three minerals. 
It will be seen that chondrodite and humite, and 
humite and clinohumite, differ in molecular composi- 
tion by the quantity, Mg.(SiO,); they form a series 
in which the increment of composition is Mg,(SiO,). 
Subtracting this increment from the composition of 
chondrodite, the residue, Mg,(SiO,), 2Mg(F,OH), is 
left. This is the composition of the mineral prolectite, 
and the increment, Mg.(SiO,), is the composition of 
the mineral forsterite. 
If the law of valency volumes be correct the equi- 
valence parameters of forsterite should be the x and y 
of the first three minerals, and a value z which is the 
difference between the z values of chondrodite and 
humite, or of humite and clinohumite; further, pro- 
lectite should have x and y values identical with those 
of the other four minerals and a zg value which is 
the difference of the z values of chondrodite and for- 
sterite. It is thus possible to calculate the equivalence 
parameters of forsterite and prolectite without using 
data determined on these two minerals, and to com- 
pare the values so obtained with those calculated from 
